The pieces:

Foot Soldier: Moves just like a pawn in chess. Promotes to a captain in the back row.
Captain: Moves one or two spaces orthogonally. Captures one or two spaces forward or one space diagonally forward. Promotes to an angel, serpent, elf or mage on the back row power square.
Elf: Moves like a rook in chess.
Angel: Moves like a knight in chess.
Serpent: Moves like a bishop in chess.
Mage: Moves like a queen in chess, but may not capture on a void (red) square.
Elven Archer: Moves or fires like a rook.
Archangel: Moves like a knight or may double this movement.
Archmage: Moves like a rook followed by a bishop, or a bishop followed by a rook. May not capture on a void (red) square.
Berserker: Moves one square orthogonally or like a bishop. Captures any number of pieces diagonally (friendly or enemy).
Emperor: Moves like a king in chess.
Dragon: Moves like a queen in chess. May pass over friendly pieces.
Spirit: Moves three spaces freely.
Sorceress: Interchanges with any friendly piece not occupying a void (red) square.
Golem: Moves one space in any direction. Captures all pieces in adjacent squares.

The Games:

Chaos (Basic Game): Checkmate the Emperor.
Occupation Chaos: The first player to occupy all five power squares wins.
Occupation and Mate Chaos: Occupy all five power squares or checkmate the Emperor.
Extinction Chaos: Eliminate all of one type of piece.
Kinglet Chaos: Eliminate all Foot Soldiers
Take-all Chaos: Eliminate all enemy pieces.
Progressive Take-all Chaos: First player gets one move, second two, first three, etc.
Double Move Chaos: Each player gets two moves per turn.